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Simplifying (5a + -2b + 7c) + (3a + b + -1c) = 0 Remove parenthesis around (5a + -2b + 7c) 5a + -2b + 7c + (3a + b + -1c) = 0 Remove parenthesis around (3a + b + -1c) 5a + -2b + 7c + 3a + b + -1c = 0 Reorder the terms: 5a + 3a + -2b + b + 7c + -1c = 0 Combine like terms: 5a + 3a = 8a 8a + -2b + b + 7c + -1c = 0 Combine like terms: -2b + b = -1b 8a + -1b + 7c + -1c = 0 Combine like terms: 7c + -1c = 6c 8a + -1b + 6c = 0 Solving 8a + -1b + 6c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 8a + -1b + b + 6c = 0 + b Combine like terms: -1b + b = 0 8a + 0 + 6c = 0 + b 8a + 6c = 0 + b Remove the zero: 8a + 6c = b Add '-6c' to each side of the equation. 8a + 6c + -6c = b + -6c Combine like terms: 6c + -6c = 0 8a + 0 = b + -6c 8a = b + -6c Divide each side by '8'. a = 0.125b + -0.75c Simplifying a = 0.125b + -0.75c
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